# Determine Bending Moment

Need help determining the bending moment acting on the column. At the top of the column, the cantilever tube is slid into a shorter piece of tubing. The shorter piece of tubing is welded to the vertical tube. I know for eccentrically loaded columns the eccentric load can be resolved to a centric force and moment. Though all of the examples I have seen for columns with an eccentric load, the cantilever part (such as a bracket) has been welded or bolted to the column. Can I the assume the bending moment is simply the load times the distance from the load to the center of the column?

• No, you can't say that with certainty, the reason in my previous answer stands - consider the beam (cantilever tube) can slide in the bracket. Albeit the effect could be small, but for operations require precision, a small amount of movement can have adverse consequence. BTW, you should issue a "new question" as you have changed the question quite a bit.
– r13
Oct 1, 2021 at 19:05

Assuming the force is placed at a distance L from the support, then the moment of the Force P with respect to the foundation will be $$M = P\cdot L$$.

If the horizontal square tubing tilts by an angle $$theta$$ then the will be equal to $$M = O \cdot L\cdot \cos\theta$$

For angle up to 10 degrees, the $$\cos \theta$$ has a minimal change ($$\cos 10^o =0.984$$), so for most intents and purposes it doesn't change.

The crucial bit is if the horizontal tubing can slide. In that case things will be different.

Q: Can I assume the bending moment is simply the load times the distance from the load to the center of the column?

A: Yes. You have to make the assumption that the cantilever and the short tubing are fitted tightly, so the resultant forces remain in the same locations throughout the process. That is, there are no excessive geometry changes at the beam-tubing interface. (I suggest you consider welding the beam to the tubing).

Q: Also, would the column length for the purpose of calculation include the height of the cantilevered tube?

A: Yes, you can include the height of the short tubing, but you shouldn't, because it complicates the process. Rather, you shall think the loading path - the cantilever causing the forces (P & M) on the short tubing, then the forces are passed to the column (below the tubing) through the welds at the column-tubing interface.

For stress check and design, you have 3 components to consider - the column, the cantilever beam, and the beam-column connection (the short tubing and welds).

Suggestion:

• For the load is dynamic in nature and frequent use - weld a cap plate to the end of the beam to prevent incidental movement. Then shim at the point "a" if necessary.

• For static load application and infrequent cycle of loading-unloading, shim at the point "a", or both points "a" and "b" should be adequate to ascertain the full point contact as assumed and calculated.

Another suggestion for light applications. Note the wall of the cantilever will govern the magnitude of the applied load.

• @bigboi Since you are using "weld" in the design, why not weld the cantilever beam directly to the column? It will be at least simpler and cleaner. If you have to stick to the current configuration, I suggest either weld the beam to the short tubing at the interface or use bolts to tie the beam and tubing together to avoid incidental movement.
– r13
Sep 15, 2021 at 13:55
• Is the beam meant to be removable? Or you are adding a beam to the existing column with the short tubing already on it? Give me some more background on why it must stay as is, then I may provide more help.
– r13
Sep 15, 2021 at 14:36
• See my updates for suggestions.
– r13
Sep 15, 2021 at 16:13

Even if the connection between the cantilever tube and the short tubing is loose and the cantilever tube will rotate a bit before it engages the bracket, it still works and imparts the same moment as long as the rotation doesn't cause it to slide off. You'd be surprised that many lifting jacks count on the biting force of a miss-aligned connection to work.

WE would measure the column height, not including the short tubing. The column is considered a column as long as there is continuity of the section along the length, so the longitudinal fibers can strain and take stress continuously.

If the short tube is not stiff enough to be considered rigid wrt. with other parts, we should try to analyze its deformation and add it to the mechanism.

When you resolve the axial load and moment you can replace the two with an off-center axial load. in many situations, it is recommended to pick a column size with a baseplate where this off-center load falls within 1/3 of the core of the column.

• If the connection is loose, there is a chance the beam will slide out of position. IMO, better safe than sorry.
– r13
Sep 15, 2021 at 2:04
• I don't agree. small angles and miss-aligned axis are taken advantage of to cause greater gripping force in many static applications such as car jacks, pile drivers. of course, moving parts require perfect alignment. Sep 15, 2021 at 2:12
• That really depends heavily on how the term "loose" is defined. Not to mention the beam can slide out of position, it potentially can rotate into a position that the upper contact point (far right corner) shifts towards the centerline of the short tubing, while the lower contact point remains the same location, thus the lever arm reduces and results in a small eccentricity. I don't think this is a mini-nature setup. For normal beam-column connections, "loose" is a dangerous thing. Well, it could be just my overthinking though.
– r13
Sep 15, 2021 at 2:33